Bibliography - M. I. Radulescu

This study investigates the initial transient hydrodynamic evolution of highly underexpanded
slit and round jets. A closed-form analytic similarity solution is derived
for the temporal evolution of temperature, pressure and density at the jet head for
vanishing diffusive fluxes, generalizing a previous model of Chekmarev using Chernyi’s
boundary-layer method for hypersonic flows. Two-dimensional numerical simulations
were also performed to investigate the flow field during the initial stages over distances
of ∼1000 orifice radii. The parameters used in the simulations correspond to the release
of pressurized hydrogen gas into ambient air, with pressure ratios varying between
approximately 100 and 1000. The simulations confirm the similarity laws derived
theoretically and indicate that the head of the jet is laminar at early stages, while
complex acoustic instabilities are established at the sides of the jet, involving shock
interactions within the vortex rings, in good agreement with previous experimental
findings. Very good agreement is found between the present model, the numerical
simulations and previous experimental results obtained for both slit and round jets
during the transient establishment of the jet. Criteria for Rayleigh–Taylor instability
of the decelerating density gradients at the jet head are also derived, as well as the
formulation of a model addressing the ignition of unsteady expanding diffusive layers
formed during the sudden release of reactive gases.

The study analyses the cellular reaction zone structure of unstable methane–oxygen
detonations, which are characterized by large hydrodynamic fluctuations and
unreacted pockets with a fine structure. Complementary series of experiments and
numerical simulations are presented, which illustrate the important role of hydrodynamic
instabilities and diffusive phenomena in dictating the global reaction rate
in detonations. The quantitative comparison between experiment and numerics also
permits identification of the current limitations of numerical simulations in capturing
these effects. Simulations are also performed for parameters corresponding to weakly
unstable cellular detonations, which are used for comparison and validation. The
numerical and experimental results are used to guide the formulation of a stochastic
steady one-dimensional representation for such detonation waves. The numerically
obtained flow fields were Favre-averaged in time and space. The resulting onedimensional
profiles for the mean values and fluctuations reveal the two important
length scales, the first being associated with the chemical exothermicity and the second
(the ‘hydrodynamic thickness’) with the slower dissipation of the hydrodynamic
fluctuations, which govern the location of the average sonic surface. This second
length scale is found to be much longer than that predicted by one-dimensional
reaction zone calculations.

Detonation waves are supersonic combustion waves. The
figures illustrate their typical unstable structure and the hydrodynamic
compressible turbulence generated via instabilities
and self-sustained by the chemical energy release. The
grayscale photographs are schlieren records of the vertical
density gradients in a methane–oxygen detonation wave, illustrating
the turbulent structure comprised primarily of
transverse shocks, shear layers, and density interfaces separating
light reacted gases and heavier unreacted gas. The
detonation propagates to the right at an average Mach number
of ˜ 6. The color figures illustrate the structure of the
wave (pressure and temperature) obtained numerically. The
front is organized in a characteristic cellular structure and
substructure, consisting of interacting triple shock Mach intersections
(frontal Mach stems, incident shocks, transversely
propagating reflected shocks, and convected shear layers). The triple points are driven by the chemical exothermicity
behind the strong Mach stems. Due to the exponential
dependence of the reaction rates on local temperature, gases
shocked by the weaker incident shocks have ignition delay
times several orders of magnitude longer, hence accumulate
as unreacted volumes behind the front. These unreacted
gases react mainly through turbulent mixing with the hot
reacted gases. Shear layers at the triple shock interactions are
Kelvin–Helmholtz unstable and promote gas ignition by turbulent
mixing of mass and heat. The transverse shocks,
which sweep perpendicularly to the main front, further disrupt
these density interfaces by the Richtmyer–Meshkov instability
involving the baroclinic torque. Unstable detonations
thus rely on compressible turbulence interactions to
promote the local reaction rates of gases which escape ignition
due to the unsteadiness of the leading front. The detonation
wave structure thus provides an excellent setting to
study exothermicity-driven compressible turbulence, manifested
primarily by the interaction of shocks, density interfaces,
and vortical flows.